   Chapter 4.5, Problem 30E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. ∫ x 3 x 2 + 1   d x

To determine

To evaluate:

The given indefinite integral x3x2+1dx.

Explanation

1) Concept:

i) The substitution rule:

If u=g(x) is a differentiable function whose range is I and f is continuous on I, then f(gx)g'xdx=f(u)du. ii) Indefinite integral

xn dx=xn+1n+1+C  n-1

iii)

ab[fx+gx] dx=abfxdx+abgxdx

iv)

abcfxdx=cabfxdx

2) Given:

x3x2+1dx

3) Calculation:

The given integral is

x3x2+1dx

Here, use the substitution method.

Substitute x2+1=u, so   x2=u-1

The differentiation gives  2xdx=du  so  xdx=du2

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